【数学】A Cubic number and A Cubic Number

A cubic number is the result of using a whole number in a multiplication three times. For example, 3×3×3=27so

$27$

is a cubic number. The first few cubic numbers are 1,8,27,64 and 125. Given an prime number p. Check that if

$p$

is a difference of two cubic numbers.

InputThe first of input contains an integer T (1T100) which is the total number of test cases.
For each test case, a line contains a prime number p (2p10^12).OutputFor each test case, output ‘YES’ if given p

$p$

is a difference of two cubic numbers, or ‘NO’ if not. 继续阅读【数学】A Cubic number and A Cubic Number

【思维/模拟】Self Numbers

In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d stands for digitadition, a term coined by Kaprekar.) For example, d(75) = 75 + 7 + 5 = 87. Given any positive integer n as a starting point, you can construct the infinite increasing sequence of integers n, d(n), d(d(n)), d(d(d(n))), …. For example, if you start with 33, the next number is 33 + 3 + 3 = 39, the next is 39 + 3 + 9 = 51, the next is 51 + 5 + 1 = 57, and so you generate the sequence
33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, …The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 has two generators, 91 and 100. A number with no generators is a self-number. There are thirteen self-numbers less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97.

Write a program to output all positive self-numbers less than or equal 1000000 in increasing order, one per line.